A particle travels along a straight line with a velocity 2 v t m s   (12 3 ) / , where t is in seconds. When t s  1 , the particle is located 10m to the left of the origin. Determine the acceleration when t s  4 , the displacement from t s  0 to t s 10 , and the distance the particle travels during this time period. 2 a m s  24 / , s m  880 , d m

a)  a = -24 m / s² , b)   Δx = 1180 m

Explanation:

a) This is a one-dimensional kinematics exercise, let's use the equation

            x = x₀ + v₀ t + ½ a t²

in this case give us the initial velocity v₀ = 2 m / s and the location (x = -10m) for t = 1 s, find us the acceleration

             a = (x-x₀- v₀ t) 2 / t²

let's calculate

             a = (-10 -0 - 2 1) 2/1²

             a = -24 m / s²

The sign of acceleration indicates that it is heading to the left; this acceleration is constant throughout the movement

therefore the acceleration for t = 4 s is also a = 24 m / s²

b) The displacement between t = 0 and t = 10 s

for t = 0     it is at x = xo

for t = 10    x = xo + 2 10 - ½ 24 10²

                  x = xo +20 -1200

                  x (10) = xo - 1180

in displacement is

     Δx = x (0) - x (10)

      Δx = 1180 m

the focus of lesson 1 is newton's first law of motion - sometimes referred to as the law of inertia. newton's first law of motion is often stated as. an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

explanation:

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.